Predictive Feedback Scheduling for Resource-Constrained Networks with Flexible Workload

Zuxin Li, Wenjun Hu School of Information Engineering

Huzhou Teachers College Huzhou, Zhejiang Province, China

{lzx, huwenjun}@hutc.zj.cn

Wanliang Wang, Bicheng Lei College of Information Engineering Zhejiang University of Technology

Hangzhou, Zhejiang Province, China wangwanliang@zjut.edu.cn, leibc@tzc.edu.cn

Abstract—Resource-constrained networks usually run in an unpredictable open environment due to the workload variations. In this paper, a predictive feedback scheduler based on least squares support vector machines (LSSVM) is proposed in order to guarantee the stability of the system. It periodically monitors the network resources, predicates the next period of available bandwidth, and adopts interpolated method to calculate the next sampling period from predicative value. Consequently, the system’s bandwidth is dynamically allocated by this feedback scheduling mechanism. Two different strategies, which are fixed bandwidth allocation and predictive feedback scheduling strategy based on LSSVM, are compared respectively. The results of simulation indicate that the proposed strategy can guarantee the stability of the system with flexible workload, and prove that the predictive feedback scheduling is an effective tradeoff method between quality of control and quality of service.

Keywords-resource-constrained networks; support vector machines; predictive feedback scheduling; flexible workload

I. INTRODUCTION In control networks with resource constraints, a set of

processing devices (i.e., sensors, actuators and controllers) in closed-loop operation usually drive one or several control tasks, which communicate data across a field-level network. These networked control systems (NCSs) specially want to have an unchangeable available bandwidth to guarantee stability of the system by providing an invariable quality of service (QoS). However, many control network applications usually run in a communication network with bandwidth constraints and unpredictable open environment, e.g., workload variations. These control networks with resource constraints and flexible workload make the analysis and design of control applications complex.

To attack this issue, there are various methodologies from different perspectives. One way is to design a suitable control technique which can compensate network-induced latency. Another way is to schedule and optimize the sharing limited resources in order to improve the system’s quality of control (QoC). Generally, static pre-established allocation strategies are adopted as bandwidth scheduling techniques in NCSs. These bandwidth allocation strategies work well because they guarantee a constant bandwidth to each control loop. However, these static strategies can not provide a given control performance in an unpredictable open environment.

Feedback scheduling strategies allow these networks to obtain a desired control performance specifications via allocating bandwidth dynamically in runtime, as reported in [1-5] and therein references. In [1], assuming an given network environment, a static optimization strategy is proposed by adjusting dynamically sampling period to improve control performance for optimal integrated control and scheduling of control system. The algorithms proposed in [2,3] adopt extending state-space model and linear programming technique to allocate the global available bandwidth to each control loop, respectively. In [4,5], the available network resources are predicated based on BP neural network technique so as to dynamically vary sampling period. Moreover, the proposed strategy in [6] uses a network monitor to obtain the current network bandwidth and the error of the network transmission. Subsequently, the next sampling period of each control loop is found by predicting the available network resources in the next period. However, these dynamical allocation strategies based on feedback mechanism work well only in a known workload.

In our scheme for control networks with flexible workload and unpredictable open environment, we propose an online predictive feedback scheduling based on least squares support vector machines (LSSVM) to adjust dynamically the bandwidth of control loop. This predictive feedback scheduling strategy is an effective tradeoff method between quality of control and quality of service.

II. SYSTEM ARCHITECTURE The system considered in this work as shown in Fig.1,

these typically spatially distributed sensors, actuators, and controllers occur through a shared resources-limited network with the feedback scheduler and other non-control nodes. The sensor nodes send messages with single packet according to sampling period pre-specified by the feedback scheduler. All actuator nodes and controller nodes are event-triggered. For control networks with workload variations and flexible application nodes, the proposed predictive feedback scheduling strategy is employed instead of traditional static pre-established allocation strategy mentioned above based on a known workload in order to guarantee the system’ stability.

The feedback scheduler mainly consists of four components: network monitor, predictor, regulator, and scheduler. The network monitor works periodically in time-triggered fashion to activate the feedback scheduler. In addition, it monitors the variations of the network condition

2009 International Conference on Measuring Technology and Mechatronics Automation

978-0-7695-3583-8/09 $25.00 © 2009 IEEEDOI 10.1109/ICMTMA.2009.97

807

and expresses to the current network utilization U(k) in order to manage the uncertainty and flexibility of network resources. The predictor based on LSSVM is responsible for making prediction of the next period value of the available network utilization U(k+1) according to current U(k) and history data. The regulator makes its decision based on the prediction of the predictor. It plays an important role in determining a new sampling period in order to have an effective tradeoff method between QoC and QoS under the network with resource constraints. The scheduler within the feedback scheduler acts as an interface with the control loop to refresh respective sampling period. From this feedback mechanism, the control system can meet a desired control performance by adjusting sampling period of the control loop according to network workload variations.

Control NetworkFlexible

Workload

Actuator i

Othernodes

Plant i

Sensor i Controller

Control Loop i

Feedback scheduler

predictornetwork monitor

scheduler

regulator

Figure 1. Feedback scheduling based system architecture

In the actual control applications, the feedback scheduler can be set as a high priority node, which shares network resources with all control loops. The scheduler refreshes sampling period of the respective control loop via networks. To reduce the network’s workload and sampling period jitters, the control period will be updated only when the absolute difference between the current value and the newly produced one exceeds a pre-specified threshold, i.e., h. In addition, the refresh period of the feedback scheduler Trefresh mainly depends on the fluctuant frequency of network workload variations and the training time of predictive algorithms.

III. ONLINE PREDICTIVE PRINCIPLE

A. LSSVM Predictive Model Assuming {dk-(M-1),…, dk} be sample data series in sliding

window at time k, where M is the number of observational sample, one point of the state vector in a state space is described as si = [dk-(M-1)+i, dk-(M-1)+ +i, …, dk-(M-1)+(m-1) +i]T according to Takens’s reconstruction theory of state space [7], where m is embedding dimension, and is delay, i = 0, 1, …, M-(m-1) -1, respectively. Therefore, the matrix of phase trajectory Sk can be described as (1) in the light of using delay coordinates theory to reconstruct phase space, where phase space dimension ( 1)N M m τ= − − , N m

kS ×∈R .

( 1) ( 1) ( 1) ( 1)0

( 2) ( 2) ( 2) ( 1)1

( ) ( )1

Tk M k M k M m

Tk M k M k M m

k

Tk M N k M N kN

d d dd d d

S

d d d

τ τ

τ τ

τ

− − − − + − − + −

− − − − + − − + −

− − − − +−

= =

ss

s

(1)

The sample set for LSSVM training can be obtained from the observational samples of the sliding window. Assuming training sample set be (xi, yi), i = k-(N-1),…, k, the input vectors xi ∈Rm-1 and output vectors yi ∈R of the LSSVM model can be given by (2), respectively.

( 1) ( 1) ( 1) ( 2)( 1)

( 2) ( 2) ( 2) ( 2)( 2)

( ) ( )

( 1) ( 1) ( 1)

( 2) ( 2) ( 1)

k M k M k M mk N

k M k M k M mk N

k M N k M N kk

k N k M m

k N k M m

k

d d dd d d

d d d

y dy d

y

τ τ

τ τ

τ τ

τ

τ

− − − − + − − + −− −

− − − − + − − + −− −

− − − − + −

− − − − + −

− − − − + −

=

=

xx

x

kd

(2)

Hence, the predictive model based on LSSVM can be described as (3) at time k,

( ) ( 1),...,i iy F i k N k= = − −x (3)

where F(·) is a required reconstructive non-linear function, which need to regress based on history data before at time k.

B. Online LSSVM Regression The complexity of the normal SVM algorithms mainly

depends on the quantity of sample data. More sample data will cause high computational cost and make against online prediction. However, LSSVM can accelerate convergent speed by solving linear functions instead of quadratic programming in SVM.

Given a training set {xi, yi}, i=k-(N-1),…, k, xi∈Rm-1, yi∈R, Suykens presented the LSSVM approach [8], in which the following function is employed to approximate the unknown function,

( )Ty x bω φ= + (4)

where 1( ) : m nφ −⋅ →R R is a nonlinear function which maps the input space to a higher dimension feature space. According to structural risk minimization principle, regression problem can be defined as optimization problem as follows,

2

, ,( 1)

1min ( , )2 2

s. t. ( )

kT

ib ei k N

Ti i i

J e e

y x b e

ω

γω ω ω

ω φ= − −

= +

= + + (5)

where is a regularization parameter and b is a constant bias. We define the Lagrangian function as

( 1)

( , , , ) ( , )

{ ( ) }k

Ti i i i

i k N

L b e a J e

a b e y

ω ω

ω φ= − −

=

− + + −x (6)

where ai is Lagrange multipliers. According to Karush- Kuhn-Tucker (KKT) optimization condition, the following equations hold,

808

00 bΤ

=e

ye (7)

where ( 1),...,T

k N kα α− −= , ( 1) ,...,T

k N ky y− −=y , [ ]1,...,1 T=e ,

( ) ( )Tmn i j ijφ φ δ γ= +x x , m=i+(N-k), n = j+ (N-k), i, j = k-

(N-1),…, k. δij = 1 when i = j and δij = 0 for otherwise. ( ) ( ) ( )T

i j i jK , φ φ=x x x x is a kernel function, which satisfies Mercer condition. Here the kernel function is

2 2( , ) exp( || || )i j i jK σ= − −x x x x . (7) can be solved directly because is positive definite.

1

1

T

Tb−

−

Ω=Ω

e ye e

(8)

1( )b−= Ωa y - e (9)

Therefore, the predictive value of the network utilization at time k+1 can be obtained.

1 1

( )( 1)

ˆ ( )

([ ,..., , ], )

k k

k

i k M N k k ii k N

U F

a K d d d bτ τ

+ +

− − + −= − −

=

= +

x

x (10)

IV. DYNAMIC REGULATION MECHANISM Generally, bandwidth allocation method must have an

effective tradeoff method between QoC and QoS. In [2-4,6], the formula U = c/h mentioned in [9] is adopted to calculate sampling period. In [2-4], the transmission time c is considered as a constant. Actually, the transmission time is a variant due to network workload variations and different media access control mechanism. For this work, an interpolated method is employed to implement the function of the regulator according to some known data.

The interpolators usually can be obtained in terms of the boundary conditions, set points, and prior knowledge. For example, when the maximal network utilization Umax is 100%, the minimum sampling period can be calculated by transmission rate and data packet size. On the other hand, the maximal sampling period hmax can be obtained by solving a maximum allowable delay bound (MADB) method [10] when the available network utilization is minimum (Umin).

Assume that the interval of network utilization is [Umin, Umax], the interpolators are ui, Umin = u0 < u1<···< un= Umax, and the relevant sampling period is hi, i = 0, 1,…, n, the following basis function according to piecewise linear interpolation method holds naturally.

1 0 1 0 10

1 1

1 1

1 1 1

( ) ( )( )

0 otherwise

( ) max min , ,0 1,..., 1

( ) ( )( )

0 otherwise

i ii

i i i i

n n n n nn

u u u u u u ul u

u u u ul u i n

u u u u

u u u u u u ul u

− +

− +

− − −

− − ≤ ≤=

− −= = −− −

− − ≤ ≤=

(11)

Hence, the regulator can decide the next sampling period to each control loop according to the predictive available network resources.

0

( ) ( )n

i ii

h u l u h=

= (12)

V. EVALUATION We consider a servo control system through a CAN field

bus. The model is given by (13).

1 1

2 2

0 1 00 20 640

x xu

x x= +

− (13)

The control law is designed by pole assignment approach without network. Its matrix coefficient K is [0.4500 0.0063]. The initial setting fixed sample period is 0.02s and the available bandwidth is 40%. The hmax is 0.0503s according to MADB approach mentioned in [10]. More details of setup are that the delay is 1, embedding dimension m calculated by false neighbors method is 4, and RBF kernel parameter σ and regularization parameter by using cross-validation method are 0.96, 6.59, respectively. The threshold of the scheduler h is 1ms. The refresh period of feedback scheduler Trefresh is 100ms.

When the feedback scheduler is activated periodically, the network bandwidth with measurement noises can be obtained by monitor. The measure value and its prediction are shown in Fig. 2, respectively. In the three intervals, network bandwidth fluctuates around 0.4, 0.7, and 0.2, respectively. Nevertheless, predictive algorithm based on LSSVM always accurately forecasts the next period of network utilization. The average training time of LSSVM only is 6.6170ms. Therefore, the proposed predictive algorithm extraordinarily suits to run online.

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1.0

Time (s)

Net

wo

rk U

tiliz

atio

n

Available Utilization

Requested - LSSVM

Requested - Fixed

Figure 2. Fig. 2 The network utilization’s measure and prediction

Given the range of available bandwidth utilization U ∈[0.15 1] and the bound of the sampling period h ∈[0.01s 0.05s], bandwidth allocation mechanism can be implemented according to piecewise linear interpolation. When fixed bandwidth allocation strategy and predictive feedback scheduling strategy are respectively employed, their response of system and the integral of the absolute error (IAE) performance criterion are shown in Fig. 3. Moreover, the

809

dynamic regulation for sampling period based on LSSVM prediction is also shown in Fig. 4.

0 1 2 3 4 5 6 7 8 90

1.0

2.0

3.0

4.0

Time (s)

Out

pu

t

LSSVM

Fixed

(a) The step response of the system

0 1 2 3 4 5 6 7 8 90

0.2

0.4

0.6

0.8

1.0

Time (s)

IAE

LSSVM

Fixed

(b) The performance of IAE

Figure 3. The step response and respective IAE

0 1 2 3 4 5 6 7 8 90

10

20

30

40

50

60

Time (s)

Sam

ple

Pe

riod

(m

s)

LSSVM

Fixed

Figure 4. Dynamic regulation for sampling period based on LSSVM

From Fig. 2 to Fig. 4 in the time interval t = 0 to 3s, the control performance is slightly impacted because the available network utilization vibrates around 0.4, as shown in Fig. 3. Still, the performance is satisfactory. From t = 3 to 6s, the results are still well thanks to redundant availability of network resources. However, the control performance of our proposed strategy is superior to the performance of fixed bandwidth allocation because the proposed strategy timely reduces the sampling period of control loop according to redundant bandwidth. From time t = 6s, the control system with fixed bandwidth allocation turns to be unstable because the available network utilization falls below the requested value of 0.4. However, the proposed strategy still can guarantee system to be stable since this predictive algorithm regulates the bandwidth consumption and dedicates to

improving QoS when the available network resources fall significantly due to workload uncertainty.

VI. CONCLUSIONS Control applications shared communication network

must meet the significant degrees of workload uncertainty, especially in resource-constrained networks. Obviously, integration of feedback control and network scheduling is an effective tradeoff method between QoC and QoS.

We present a predictive feedback scheduling strategy based on LSSVM in order to handle uncertain and flexible workload in the control networks according to the availability of network resources. It is highlight that the proposed method allows the control applications to be highly flexible with respect to workload variations, while improving the control performance to the maximum extent. Moreover, this predictive algorithm keeps the computing overhead relatively small, which is very suitable for online prediction.

ACKNOWLEDGMENT This work was supported by the National Natural Science

Foundation of China under Grants 60573123, 60872057, and by the Zhejiang Provincial Natural Science Foundation of China under grant Y107293.

REFERENCES [1] M. Branicky, S. Philips, and W. Zhang, “Scheduling and feedback co-

design for networked control systems,” Proc. of the IEEE Conference on Decision and Control, IEEE Press, Dec. 2002, pp.1211-1217.

[2] M. Velasco, J. M. Fuertes, C. Lin, P. Marti, and S. Brandt, “A control approach to bandwidth management in networked control systems,” Proc. of the Annual Conference of the IEEE Industrial Electronics Society, IEEE Press, Nov. 2004, pp.2343-2348.

[3] M. Velasco, P. Marti, and M.Frigola, “Bandwidth management for distributed control of highly articulated robots,” Proc. of the IEEE International Conference on Robotics and Automation, IEEE Press, Apr. 2005, pp. 265-270.

[4] W. H. Zhao and F. Xia, “A neural network approach to QoS management in networked control systems over Ethernet,” Lecture Notes in Control and Information Sciences, vol.344,2006,pp.444-449.

[5] J. Yi, Q. Wang, D. Zhao, and J. T. Wen, “BP neural network prediction-based variable-period sampling approach for networked control systems,” Applied Mathematics and Computation, vol.185, Feb. 2007, pp.976-988.

[6] Y. Wang, H. Cai, Q. W. Chen, and W. L. Hu, “Feedback scheduler design of networked control systems,” Acta Electronica Sinica, vol.35, Feb. 2007, pp.379-384. (in Chinese)

[7] F. Takens, “Detecting strange attractors in fluid turbulence,” Dynamical Systems and Turbulence, D. Rand and L. S. Young editors, Belin: Springer-Verlag, 1981, pp.366-381.

[8] J. A. K. Suykens and J. Vandewalle, “Least squares support vector machines classifiers,” Neural Processing Letters, vol.9, Jun. 1999, pp.293-300.

[9] W. Zhang, “Stability analysis of networked control systems,” Ph.D. dissertation, Case Western Reserve University, USA, 2001.

[10] Z. X. Li, W. L. Wang, B. C. Lei, and H. Y. Chen, “An approach to bandwidth management based on fuzzy logic,” Engineering Science, vol.10, Jul. 2008, pp.104-111. (in Chinese)

810